Please clearly label each answer. little explanation is needed The amount of tim
ID: 3365424 • Letter: P
Question
Please clearly label each answer. little explanation is needed
The amount of time a bank teller spends with each customer has a population mean, , of 2.90 minutes and a standard deviation, , of 0.40 minute. Complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table Click here to view page 2 of the cumulative standardized normal distribution table a. If you select a random sample of 25 customers, what is the probability that the mean time spent per customer is at least 2.7 minutes? (Round to four decimal places as needed.) b. If you select a random sample of 25 customers, there is an 85% chance that the sample mean is less than how many minutes? Round to four decimal places as needed.) c. What assumption must you make in order to solve (a) and (b)? A. That the population is normally distributed B. That the sample is symmetrically distributed such that the Central Limit Theorem will likely hold ° C. That the sample is normally distributed D. That the population is uniformly distributed 0 E. That the population is symmetrically distributed such that the Central Limit Theorem will likely hold for samples of size 2 d. If you select a random sample of 64 customers, there is an 85% chance that the sample mean is less than how many minutes? Round to four decimal places as needed.)Explanation / Answer
a) std error of mean =std deviation/(n)1/2 =0.4/(25)1/2 =0.08
therefore probability=P(X>2.7)=1-P(X<2.7)=1-P(Z<(2.7-2.90)/0.08)=1-P(Z<-2.5)=1-0.0062 =0.9938
b)
for lowest 15 percentile ; zscore =-1.0364
therfore corresponding value =mean +z*Std deviation =2.9-1.0364*0.08 =2.8171
c)
option E is correct
d)
) std error of mean =std deviation/(n)1/2 =0.4/(64)1/2 =0.05
for lowest 15 percentile ; zscore =-1.0364
therfore corresponding value =mean +z*Std deviation = 2.8482